In particular, you get the exact version of the library you want. If you've ever had the experience of trying to make your software work with multiple versions of its dependencies because different OSes ship with different versions, then you'll know how annoying this is.
This is particularly true of run-time problems. If they don't compile, then that's relatively easy to fix. If there's a difference at run-time, its often way more expensive to fix.
With a package manager, you get the exact version, but you also can use different versions for different apps on your system. You can also upgrade without breaking other apps (new security version) or not upgrade if there's some good reason not to.